Question

How many 4 digit even numbers have all 4 digits distinct ?

• A. 2240
• B. 2296
• C. 2620
• D. 4536

Answer 1

The correct option is B 2296

The digits are given to be distinct i.e. no repetition. 4 digit even numbers cannot start with 0 and must end with 0, 2, 4, 6, or 8.
Since there is a condition for 0 in starting as well as ending we will count the even numbers ending with 0 seperately.
So the total number of 4 digit even number = 4 digit even numbers ending with zero + 4 digit even numbers ending with 2, 4, 6, 8.
4 digit even numbers ending with 0


4 digit even numbers ending with 2, 4, 6, 8


So the total number of 4 digit even numbers
= 504 + 1792 = 2296.